Agreed the wind, rain, and snow being "football & part of the Bills ID" is a fairy tale for a franchise that outside of the 90s has qualified for the playoffs 12 times in 5 decades.
I'm sure this myth got started during the years where the Bills would beat or play close a team that was superior, except the bad weather kept it close. Unfortunately the fans bought in to it, and told their kids of how this was "Buffalo football". This kept going and now the "weather" is this sacred aspect to football, where today's football (especially the way this team is built) kills the game.